The government is not a family (or a business), the budgets don't work the same.
Income equals spending. This is an absolute truth.
If spending goes down (people and businesses stop buying stuff) income goes down (wages fall and jobs disappear).
There are three options for the government at that point:
Do nothing and hope that the economy sorts itself out.
Encourage additional spending with lower taxes, lower interest rates, and quantitative easing
Direct stimulation of the economy by spending more on infrastructure, education, defense, energy, etc.
It did not look to anyone studying the situation that the economy would sort itself out anytime soon. Economy was contracting at a very high rate. Using a combination of options 2 and 3 was the best solution.